# CTPQRT (3) - Linux Man Pages

ctpqrt.f -

## SYNOPSIS

### Functions/Subroutines

subroutine ctpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
CTPQRT

## Function/Subroutine Documentation

### subroutine ctpqrt (integerM, integerN, integerL, integerNB, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldt, * )T, integerLDT, complex, dimension( * )WORK, integerINFO)

CTPQRT

Purpose:

CTPQRT computes a blocked QR factorization of a complex
"triangular-pentagonal" matrix C, which is composed of a
triangular block A and pentagonal block B, using the compact
WY representation for Q.

Parameters:

M

M is INTEGER
The number of rows of the matrix B.
M >= 0.

N

N is INTEGER
The number of columns of the matrix B, and the order of the
triangular matrix A.
N >= 0.

L

L is INTEGER
The number of rows of the upper trapezoidal part of B.
MIN(M,N) >= L >= 0.  See Further Details.

NB

NB is INTEGER
The block size to be used in the blocked QR.  N >= NB >= 1.

A

A is COMPLEX array, dimension (LDA,N)
On entry, the upper triangular N-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the upper triangular matrix R.

LDA

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

B

B is COMPLEX array, dimension (LDB,N)
On entry, the pentagonal M-by-N matrix B.  The first M-L rows
are rectangular, and the last L rows are upper trapezoidal.
On exit, B contains the pentagonal matrix V.  See Further Details.

LDB

LDB is INTEGER
The leading dimension of the array B.  LDB >= max(1,M).

T

T is COMPLEX array, dimension (LDT,N)
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks.  See Further Details.

LDT

LDT is INTEGER
The leading dimension of the array T.  LDT >= NB.

WORK

WORK is COMPLEX array, dimension (NB*N)

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

April 2012

Further Details:

The input matrix C is a (N+M)-by-N matrix

C = [ A ]
[ B ]

where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
upper trapezoidal matrix B2:

B = [ B1 ]  <- (M-L)-by-N rectangular
[ B2 ]  <-     L-by-N upper trapezoidal.

The upper trapezoidal matrix B2 consists of the first L rows of a
N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
B is rectangular M-by-N; if M=L=N, B is upper triangular.

The matrix W stores the elementary reflectors H(i) in the i-th column
below the diagonal (of A) in the (N+M)-by-N input matrix C

C = [ A ]  <- upper triangular N-by-N
[ B ]  <- M-by-N pentagonal

so that W can be represented as

W = [ I ]  <- identity, N-by-N
[ V ]  <- M-by-N, same form as B.

Thus, all of information needed for W is contained on exit in B, which
we call V above.  Note that V has the same form as B; that is,

V = [ V1 ] <- (M-L)-by-N rectangular
[ V2 ] <-     L-by-N upper trapezoidal.

The columns of V represent the vectors which define the H(i)'s.

The number of blocks is B = ceiling(N/NB), where each
block is of order NB except for the last block, which is of order
IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
for the last block) T's are stored in the NB-by-N matrix T as

T = [T1 T2 ... TB].

Definition at line 189 of file ctpqrt.f.

## Author

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